Parameterised eight order iterative structures requiring no function derivative for solving nonlinear equation

In this work, the function derivatives in the double Newton iterative structure were annihilated by the use of function estimation with polynomial interpolation and divided difference operator. This resulted in the development of a modified double Newton iterative structure that requires no function derivative. To enhance the modified double Newton iterative structure, it was composed with an iterative structure that involves weight functions and requires an additional function evaluation to produce two parameterized families of iterative structures with convergence order eight. The conditions for convergence of the developed iterative structures were established via the Taylor series approach. The applicability of the developed iterative structures was tested on some nonlinear equations and from the obtained computational results, they are highly competitive when compared with some good existing iterative structures of the same order of convergence.

کلیدواژه ها:

Iterative structure ، Newton iterative structure ، Derivative free ، divided difference ، Polynomial interpolation ، Weight function